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    Statistics of Parameter Estimates: A Concrete Example

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    Type
    Article
    Authors
    Aguilar, Oscar
    Allmaras, Moritz
    Bangerth, Wolfgang
    Tenorio, Luis
    KAUST Grant Number
    KUS-C1-016-04
    Date
    2015-01
    Permanent link to this record
    http://hdl.handle.net/10754/599732
    
    Metadata
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    Abstract
    © 2015 Society for Industrial and Applied Mathematics. Most mathematical models include parameters that need to be determined from measurements. The estimated values of these parameters and their uncertainties depend on assumptions made about noise levels, models, or prior knowledge. But what can we say about the validity of such estimates, and the influence of these assumptions? This paper is concerned with methods to address these questions, and for didactic purposes it is written in the context of a concrete nonlinear parameter estimation problem. We will use the results of a physical experiment conducted by Allmaras et al. at Texas A&M University [M. Allmaras et al., SIAM Rev., 55 (2013), pp. 149-167] to illustrate the importance of validation procedures for statistical parameter estimation. We describe statistical methods and data analysis tools to check the choices of likelihood and prior distributions, and provide examples of how to compare Bayesian results with those obtained by non-Bayesian methods based on different types of assumptions. We explain how different statistical methods can be used in complementary ways to improve the understanding of parameter estimates and their uncertainties.
    Citation
    Aguilar O, Allmaras M, Bangerth W, Tenorio L (2015) Statistics of Parameter Estimates: A Concrete Example. SIAM Review 57: 131–149. Available: http://dx.doi.org/10.1137/130929230.
    Sponsors
    The work of this author was partially supported by award KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).The work of this author was partially supported by NSF grant DMS-0914987.
    Publisher
    Society for Industrial & Applied Mathematics (SIAM)
    Journal
    SIAM Review
    DOI
    10.1137/130929230
    ae974a485f413a2113503eed53cd6c53
    10.1137/130929230
    Scopus Count
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